Digital watermarking is an emerging research area for copyright protection of electronic documents and media, which is one of the most important problems to be solved in the cyberspace society. A statistic approach for embedding and extracting a digital watermark on an image is proposed. This approach is based on the realization that a stego-image after watermark attacks should preserve the characteristics of the stego-image if the stego-image after attacks retains its commercial values. In other words, the appearance of the image after attacks is still clearly visible and similar to the original image. This kind of preservation can be reflected as the variances of color levels of pixels both in stego-without-attacks- and stego-with-attacks- images are most likely the same. The embedded digital watermark by this approach seems robust after several attacks are performed on the stego-image.